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TS EAMCET · Maths · Indefinite Integration

If \(\int \frac{d x}{(1+\sqrt{x}) \sqrt{x-x^2}}=\frac{A \sqrt{x}}{\sqrt{1-x}}+\frac{B}{\sqrt{1-x}}+C\), where \(C\) is real constant, then \(A+B\) equals to

  1. A \(3\)
  2. B \(0\)
  3. C \(1\)
  4. D \(2\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(0\)

Step-by-step Solution

Detailed explanation

Given, \[ \int \frac{d x}{(1+\sqrt{x})\left(\sqrt{x^2-x^2}\right)}=\frac{A \sqrt{x}}{\sqrt{1-x}}+\frac{B}{\sqrt{1-x}}+c \] On differentiating both sides, we get…